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Tutorial

This tutorial will cover the difference between a one-way ANOVA test versus a test with a two-way ANOVA. You’ll learn about:

One-way ANOVA

Two-way ANOVA

1. One-way ANOVA

Recall what ANOVA is: in many tests, you want to compare three or more population means and see if there's a significant difference between the means. The procedure for comparing three or more population means is called Analysis of Variance, also called ANOVA.

Suppose that you had some 10 point cleanliness scale that we were ranking detergents on.

Based on this one factor, detergent, you are trying to see how clean the clothes get on average.

This is not enough information to actually run an ANOVA test. You would need more information than just this, but this is a situation which would lead you to an ANOVA test.

Because we're only looking at the one factor of detergent affecting cleanliness, in this case, this is called a one-way ANOVA.

One-Way ANOVA

A hypothesis test that compares three or more population means with respect to a single characteristic or factor.

2. Two-way ANOVA

Now, suppose that you included water temperature.

It's possible that some of these detergents do a better job of cleaning in different temperatures of water.

Now that you have all of this additional information, you're actually looking at 12 treatments for detergents and three water temperatures for each detergent. There are two factors that are factoring into the cleanliness score.

Because there are two factors that are affecting the cleanliness score, we can still do an ANOVA test. But this time, it's called a two-way ANOVA.

Two-Way ANOVA

A hypothesis test that compares three or more population means with respect to multiple characteristics or factors.

Again, there's not enough information here to actually run the test. But this is a situation that would give rise to a two way ANOVA.

In one-way ANOVA, you can consider population means that are based on just one characteristic. In two-way ANOVA, you consider the comparisons based on multiple characteristics or factors.

Thank you and good luck!

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

Terms to Know

One-Way ANOVA

A hypothesis test that compares three or more population means with respect to a single characteristic or factor.

Two-Way ANOVA

A hypothesis test that compares three or more population means with respect to multiple characteristics or factors.